Min-Max Certainty Equivalence Principle and Differential Games
نویسندگان
چکیده
This paper presents a version of the Certainty Equivalence Principle, usable for nonlinear, variable end-time, partial observation Zero-Sum Differential Games, which states that under the unicity of the solution to the auxiliary problem, optimal controllers can be derived from the solution of the related perfect observation game. An example is provided where in one region, the new extended result holds, giving an optimal control, and in another region, the unicity condition is not met, leading indeed to a non-certainty equivalent optimal controller.
منابع مشابه
Stochastic nonlinear minimax dynamic games with noisy measurements
This note is concerned with nonlinear stochastic minimax dynamic games which are subject to noisy measurements. The minimizing players are control inputs while the maximizing players are square-integrable stochastic processes. The minimax dynamic game is formulated using an information state, which depends on the paths of the observed processes. The information state satisfies a partial differe...
متن کاملAdaptive Mean Field Games for Large Population Coupled ARX Systems with Unknown Coupling Strength
This paper is concerned with decentralized tracking-type games for large population multi-agent systems with mean-field coupling. The individual dynamics are described by stochastic discrete-time auto-regressive models with exogenous inputs (ARX models), and coupled by terms of the unknown population state average (PSA) with unknown coupling strength. A two-level decentralized adaptive control ...
متن کاملLarge Population Stochastic Dynamic Games: Closed-loop Mckean-vlasov Systems and the Nash Certainty Equivalence Principle
Abstract. We consider stochastic dynamic games in large population conditions where multiclass agents are weakly coupled via their individual dynamics and costs. We approach this large population game problem by the so-called Nash Certainty Equivalence (NCE) Principle which leads to a decentralized control synthesis. The McKean-Vlasov NCE method presented in this paper has a close connection wi...
متن کاملLarge-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence Principle
We consider linear-quadratic-Gaussian (LQG) games with a major player and a large number of minor players. The major player has a significant influence on others. The minor players individually have negligible impact, but they collectively contribute mean field coupling terms in the individual dynamics and costs. To overcome the dimensionality difficulty and obtain decentralized strategies, the...
متن کاملAn Invariance Principle in Large Population Stochastic Dynamic Games
We study large population stochastic dynamic games where the so-called Nash certainty equivalence based control laws are implemented by the individual players. We first show a martingale property for the limiting control problem of a single agent and then perform averaging across the population; this procedure leads to a constant value for the martingale which shows an invariance property of th...
متن کامل